Often information on a patient's condition prior to receiving some treatment or having some operation performed may be known (sometimes called the covariables for an individual) and this concomitant information should be incorporated into one's analysis of survival data. This proposed research will examine several aspects of this problem when there are k (greater than 1) causes competing for the failure of an individual. First, it is proposed to work out a method to decide which of the covariables merit inclusion into the model, i.e., make some inferential statements regarding the coefficients of the covariables. A second purpose of this study would be to provide the framework for analyzing such data when the underlying life distributions possessed the property of proportional failure rate. Finally, it would be desirable to examine the implications of incorporating such concomitant information in the estimation of various probabilities in competing risk theory.